Interresting physics...

[Structural Integrity]

If you had an object, floating about in space, with a barbell structure and two different masses at each end, would it have a gravitational force of a single object?

For example:

Barbell: 

+--------O

3 miles wide
in gravity less environment (ie, no other gravitational forces than only the barbell)
Two point masses at each end, right hand mass being 4 times heavier than left hand mass. Shaft is weightless...
Acceleration of barbell is 0

If you were to place a third object on the centre of mass, would it remain in the same position, or would it be pulled to the right?

I just came across this problem, but personally I think the third object would stay put... I don't know why... It just feels right...
I find it hard to imagine that the gravitational force of any object is different at another position. Think about it... if it was then an object at the CENTRE_OF_MASS point of our planet would be weightless.... wait.... eh...

[at0mic.c0w]

Originally posted by Structural Integrity
If you were to place a third object on the centre of mass, would it remain in the same position, or would it be pulled to the right?

it would be pulled towards the heavier object. just imagine placing an object in the center of mass between the earth and the moon.

Originally posted by Structural Integrity
Think about it... if it was then an object at the CENTRE_OF_MASS point of our planet would be weightless.... wait.... eh...

if u think of the earth as a perfect sphere then the center of mass is also the place where the gravitational forces of the earth cancel each other out.

[Nodrog]

Despite having no knowledge of the area, and absolutely nothing that would give my opinion any credibility or reason why you should listen to it, I would imagine the object would be pulled to the right, if the barbell on the right had sufficient mass. You cant just tie a light thing to a heavy thing with a piece of string and then claim its a single object.

Spheres are different, because they can be treated as point masses due to special Newton magic (ie, this planet).

[Gayle29uk]

^^^ what he said.

[queball]

It is different from two seperate objects, since they would otherwise accelerate towards each other. At the centre of gravity there is no net gravitational force so an object wouldn't move. Nod's disclaimer too.

[W]

Originally posted by Structural Integrity
If you had an object, floating about in space, with a barbell structure and two different masses at each end, would it have a gravitational force of a single object?

For example:

Barbell: 

+--------O

3 miles wide
in gravity less environment (ie, no other gravitational forces than only the barbell)
Two point masses at each end, right hand mass being 4 times heavier than left hand mass. Shaft is weightless...
Acceleration of barbell is 0

If you were to place a third object on the centre of mass, would it remain in the same position, or would it be pulled to the right?

I just came across this problem, but personally I think the third object would stay put... I don't know why... It just feels right...
I find it hard to imagine that the gravitational force of any object is different at another position. Think about it... if it was then an object at the CENTRE_OF_MASS point of our planet would be weightless.... wait.... eh...

Depends on the mass of the objects*. If they're the same mass, then an object placed right in the middle will not immediately feel any gravitational forces (it will soon enough tho, as that point isn't gravitationally stable).

So no, simply physically connecting two masses does not make it give of the gravity of a single point mass. Take a hollow sphere for instance, inside it, all gravity cancels out, as long as the sphere is of homogeneous density. You wouldn't fall to the center, nor would you fall towards the edge. (which is the reason for the effect that gravity lessens the deeper you go into a mine into the earth. Not that the effect is noticable to humans before you reach magma...)


*) You said one was 4 times heavier than the other, but since they're in a gravityless environment, that would mean one would weigh 0 newton, and the other 4*0 newton=0 newton. They would cause eachother to excert a force on the shaft tho, but that force would be the same for both masses.

[Nodrog]

Originally posted by W

*) You said one was 4 times heavier than the other, but since they're in a gravityless environment, that would mean one would weigh 0 newton, and the other 4*0 newton=0 newton. They would cause eachother to excert a force on the shaft tho, but that force would be the same for both masses.

I assume he meant "No external objects exerting any gravitational force on any of the objects in this system" rather than "gravityless"...

[W]

Originally posted by Nodrog
I assume he meant "No external objects exerting any gravitational force on any of the objects in this system" rather than "gravityless"...

Me too.

[Structural Integrity]

Originally posted by at0mic.c0w
it would be pulled towards the heavier object. just imagine placing an object in the center of mass between the earth and the moon.

I did some more research on the subject, and yes, it will be pulled to the heavier point because each end is treated as a seperate system. I read that the third object will only remain constant in the gravitational equilibrium.

Anyway, to get this subject a tad nearer to what I'm working on ATM:
If you have two objects, with a random shape, added together (in a barbell way for the heck of it), each with two different masses. The objects are homogenous though (ie: same mass at every point of the object)
In this case both objects DO have a volume, which is unknown (and will not be known either since it's too much work to calculate ).
What we DO know however are the points (coordinates) that make up each object.

how would one calculate the centre of mass of both added objects?
And what for adding three objects together?

[W]

Originally posted by Structural Integrity
I did some more research on the subject, and yes, it will be pulled to the heavier point because each end is treated as a seperate system. I read that the third object will only remain constant in the gravitational equilibrium.

Anyway, to get this subject a tad nearer to what I'm working on ATM:
If you have two objects, with a random shape, added together (in a barbell way for the heck of it), each with two different masses. The objects are homogenous though (ie: same mass at every point of the object)
In this case both objects DO have a volume, which is unknown (and will not be known either since it's too much work to calculate ).
What we DO know however are the points (coordinates) that make up each object.

how would one calculate the centre of mass of both added objects?
And what for adding three objects together?

Apart from utterly simple geometric shapes (ie symetric about atleast two planes/axes) you can't even find the center of mass of a single object. Finding the center of mass for two objects with known centers of mass is dead easy tho. It's on the line between the two centers of mass, at the point where M/x^2=m/(d-x)^2


OBS! If you want to know how a third object would rotate/be affected by any nonsphere object, you're on the entirely wrong path. It is not enough to know the center of mass, you have to integrate the gravity force over all the shapes.

[Structural Integrity]

Hmmmmm.... *thinks*

What if one were to average and add each point that makes up the object. Then the average being the centre of mass (and the centre of the object, since it's homegenous)

If I were to this for a triangle for example, I'd take (point_1 / 3) + (point_2 / 3) + (point_3 / 3)... Wouldn't that give me the centre of the object, which is equal to the centre of mass?
I haven't drawn this out yet as I'm off for home in a few minutes, but it seems sensible...

As for the centre of gravity part for 3+ bodies.... that's one thing I can't think of that quickly either....

[W]

Forgive me, I was wrong on the center of gravity problem too.

S-I, you need to learn about the integrals. No way around it. I have a feeling you won't be dealing with simplified cases like single spheres or two spheres in orbit around eachother.

[Structural Integrity]

Originally posted by W
Forgive me, I was wrong on the center of gravity problem too.

S-I, you need to learn about the integrals. No way around it. I have a feeling you won't be dealing with simplified cases like single spheres or two spheres in orbit around eachother.

***home***

OI, of the one maths subject I REALLY dispise, you pick that one... (altho I can handle it for "simple" quadratic equations).
Although I cannot place integrals in the subject just this instance =/

Anyway, I drew out some points on paper, adding the coords together and dividing it by the amount of points, and it SEEMS as if I get the centre of the object (altho this IS quite logical).
I assume that using a silhoutte, or concave object, for this will give the centre of the object aswell as the centre of mass. But using a convex object will only give the centre of mass (not the centre of the object. I'm not 100% sure about this as I cannot think of a way to test it.

[Ragnarak]

if this is for your games engine you just have to decide how complicated you need to make it to LOOK realistic

even something like a simple solid metal cuboid orbiting the earth would experience different forces due to the gravity of the earth at the nera and far points.

'the gravitational force of a single object' is just another simplification

for an object of uniform density the centre of the object is the centre of mass is it not? isn't that how you define what the centre of the object is?

[Structural Integrity]

Yeh, it's basically for my game-engine, but I've noticed that the physics are NOT going to be the main calculation problem (when I look at the speed issue) so I don't mind putting some maths in it. The main problem will be collision detection as a whole (when working on polygon level).

I was asking this because I want to calculate the centre of gravity for collision reaction. For example when I hit a cube at one of it's points with a vector the cube will react with a rotation as well as acceleration.
To determine the amount of energy that is put in rotation I need the centre of mass, the distance and direction from the centre of mass to the collision point, the mass of the entire object itself and the force of the collision.

I don't feel like predefining the centre of mass since it should be possible to calculate, and it will be a one-time calculation anyway (at load up).

As for adding two (or more) objects together, with different masses... this could be done for example when making a model. Imagine a space ship model with a seperate turret on it that can rotate. The turret is an object, as well as the rest of the ship, but will have a different mass AND different centre of gravity. So I need to calculate the common centre of mass.

Whilst writing this something popped in my mind:
If one were to inflict a force, on an non-homogenous object like the barbell, is the new rotation then AROUND the COMMON centre of mass?
Sounds logical... though I'm no physisist (sp?) so I cannot prove this

[queball]

Taking the average of the vertices doesn't give the centre of mass. Imagine changing one corner of an object to add more vertices but not change the shape much, your average will move towards that corner even though the distribution of mass hasn't changed much. If you can split an object up into tetrahedra you should be able to get the center of mass. If you're going to look at rotation caused by an impulse, you need to look at moments of inertia.

[Structural Integrity]

Originally posted by queball
Taking the average of the vertices doesn't give the centre of mass. Imagine changing one corner of an object to add more vertices but not change the shape much, your average will move towards that corner even though the distribution of mass hasn't changed much. If you can split an object up into tetrahedra you should be able to get the center of mass. If you're going to look at rotation caused by an impulse, you need to look at moments of inertia.

True... I just thought about it again....
If an object has tons of vertices on one side the centre of mass will pulled to that side. So this won't work....

[W]

This is a problem I've worked some on (the rotation+impulse one), just in 2d, and even then it's hell (I tried making a realistic "bouncing ball" effect for a square/triangle/other polygon)

I guess I'll look some into it now. Btw, how the hell are you going to do the rotation now? With the axis of rotation unaligned with the unit vectors of the universe, you're gonna have to do some costly calculations to find the rotation matrix even after you know the axis. If all the rotation axis is even solveable as rotation matrixes

[Structural Integrity]

Originally posted by W
This is a problem I've worked some on (the rotation+impulse one), just in 2d, and even then it's hell (I tried making a realistic "bouncing ball" effect for a square/triangle/other polygon)

I guess I'll look some into it now. Btw, how the hell are you going to do the rotation now? With the axis of rotation unaligned with the unit vectors of the universe, you're gonna have to do some costly calculations to find the rotation matrix even after you know the axis. If all the rotation axis is even solveable as rotation matrixes

wait, that went straight over my head...

I was thinking of representing the force as a 3D vector, then calculating the angle between the centre_of_mass and impact_point, and the force vector.
With this angle you should be able to say how much force goes in rotation and how much force goes in movement...
/me opens his MS paint

http://www.geocities.com/structual/bla.html?phys1.jpg

As you can see is it possible to disband the x and y factor of the force and those can be projected seperately on the impact point. The Y factor is in this case irrelevant since it is parallel to the impact plane.
With the mass of the object, and the force of the... eh, force you can calculate how much energy is needed to accelerate the impact point. With this acceleration you basically MOVE the IMPACT POINT.
Next step is to see how much energy is changed in movement and how much is changed in rotation. I think this can be best done with the lever I have drawn, but I haven't worked out exactly on how I plan on doing this... (although I think it involves in drawing a perpendicular line from the accelerationpoint to the X-factor of the force (and other factors if they play a role)
Use the angle between the X-factor and the impactpoint-centre-line to determine the change in speed. The smaller the angle, the less force is changed into movement, the more is changed into rotation.
Think of yourself pushing a pen at the tip.
If the centre of mass is at 0, and the tip is a infinity, all force will be changed to rotation, and none to movement.

I have no idea if any of this would work, but it seems sensible enough to me.

[W]

Well, that doesn't quite make sense to me. If you push a pen at the tip, the same amount of energy would go to movement versus rotation no matter how long the pen is. It's the shape and where you push it that determines that.

Anyway, what about friction? Say if two equal spheres hit eachother not-head-on, then the friction and elasticity of the matterials would determine how they bounced, and whether any energy went into rotation or not. Collitions is messy stuff.

I figured out how to do the actual rotation of the object tho, that's pretty easy.

[Structural Integrity]

Originally posted by W
Well, that doesn't quite make sense to me. If you push a pen at the tip, the same amount of energy would go to movement versus rotation no matter how long the pen is. It's the shape and where you push it that determines that.

I was talking about a hypothetical pen, where you would push it at +infinity
The TOTAL energy put into the object is the same... but the energy put in rotation or movement is different.
What if you push the pen EXACTLY on it's centre of mass... there would be no rotation, only movement. The further away you push, the more energy will go in rotation.

Anyway, what about friction? Say if two equal spheres hit eachother not-head-on, then the friction and elasticity of the matterials would determine how they bounced, and whether any energy went into rotation or not. Collitions is messy stuff.

I figured out how to do the actual rotation of the object tho, that's pretty easy. [/b]

Imagine a bounce with friction... presume one sphere is NOT moving... Sphere2 has only movement over the Y axis.
If sphere2 hits sphere1 on its right, there will new movement as well as new rotation (because of the friction)
I think that friction can be best thought of as a scalar value that determines how much of the vector energy is changed to friction. A high number would result in much friction, thus much loss in energy from the sphere that had the energy in the first place, and a low number would make the bump smoother and result in less loss from the sphere with the initial energy.

http://www.geocities.com/structual/bla.html?phys2.jpg

If I would model something like that I'd do it as in the picture.
If there was much friction (100%) then the bottom sphere would lose ALL of it's energy and the top sphere would get a motion in the direction "NEW MOVEMENT" and the outer edge of the sphere would spin at the same speed as the magnitude of the "FRICTION" vector.
With 0 friction the upper sphere would only get movement, and the bottom sphere would remain to move only with a new direction (and I think that is the same direction as the "FRICTION" vector points to).

Again, I don't know if any of the above is true as I haven't studied the subject, but it all seems quite logical to me.

[Cyp]

[nomath]A force acting on an object causes the object to move. Where on the object the force acts does not affect what the change in velocity of the object is.

It's just harder to apply a force a long way from the centre of mass than it is at the centre of mass, since the object won't resist the force you apply.

That is, if you push a pen with a constant force 1N, the pen has the same acceleration, no matter where you push, but if you don't push the centre, it will start rotating, the point you push at will be moving away from you faster due to the rotation, so you have to push faster to push with the same force.[/nomath]

[W]

Originally posted by Structural Integrity
I was talking about a hypothetical pen, where you would push it at +infinity
The TOTAL energy put into the object is the same... but the energy put in rotation or movement is different.
What if you push the pen EXACTLY on it's centre of mass... there would be no rotation, only movement. The further away you push, the more energy will go in rotation.



Imagine a bounce with friction... presume one sphere is NOT moving... Sphere2 has only movement over the Y axis.
If sphere2 hits sphere1 on its right, there will new movement as well as new rotation (because of the friction)
I think that friction can be best thought of as a scalar value that determines how much of the vector energy is changed to friction. A high number would result in much friction, thus much loss in energy from the sphere that had the energy in the first place, and a low number would make the bump smoother and result in less loss from the sphere with the initial energy.

http://www.geocities.com/structual/bla.html?phys2.jpg

If I would model something like that I'd do it as in the picture.
If there was much friction (100%) then the bottom sphere would lose ALL of it's energy and the top sphere would get a motion in the direction "NEW MOVEMENT" and the outer edge of the sphere would spin at the same speed as the magnitude of the "FRICTION" vector.
With 0 friction the upper sphere would only get movement, and the bottom sphere would remain to move only with a new direction (and I think that is the same direction as the "FRICTION" vector points to).

Again, I don't know if any of the above is true as I haven't studied the subject, but it all seems quite logical to me.

Doesn't really work that way, no. Look into elastic and nonelastic collisions; energy is always conserved, but not always momentum. And in 3D, there is always more than one solution if you just use the conservation laws. Of course, I haven't seen how it looks when you do it your way, it might look realistic, but I have a feeling it will look stupid in most non-constructed cases. I do suggest reading up on the mechanics tho (I really should go back to the books myself, don't remember 90% of it)

Found this in my sig!

[queball]

Originally posted by W
energy is always conserved, but not always momentum.

what?!?
Energy is always conserved, momentum is always conserved; kinetic energy can be transformed though.

[W]

Originally posted by queball
what?!?
Energy is always conserved, momentum is always conserved; kinetic energy can be transformed though.

Yes, sorry, other way around, of course.

[Structural Integrity]

I ordered a maths book for 3D programming this sunday and am waiting for it to arive... I hope it covers a good deal of physics too.

I gave the 2 spheres thing some more thought and there's a tad of a flaw in the fact that the second sphere will ALSO get a rotation, which makes it a tad more difficult

I'm going to catch up on my physics as well... seems as if I got a lot to do the coming few weeks

[acropolis]

The day I'm playing a video game and suddenly my character is pulled off the earth and through orbit by the gravitational pull of the moon is the day I can be sure SI has made it big time.